What is the difference between a path and a bezier?
There are 2 main category:


Bezier
Nurbs


They differ in calculations.

Each is a preset for its category:


Bezier: It is a normal bezier curve with 2 splines,it is usually what you start with,It uses aligned handle.
Circle: It is a preset of Bezier that form a circle,It uses automatic handle type.
NurbsCurve: Nurbs are different in calculations,you can read the different here.
NurbsCircle: A circle formed by nurbs and is cyclic,made out of 8 control points.
Path: Is a very simple Nurbs,It can be used to create motion paths for objects when doing animations,It is very fast to edit.